Final answer:
To simplify cosh(ln t), express ln t in terms of hyperbolic functions and then apply the properties of hyperbolic functions to simplify the expression.
Step-by-step explanation:
To simplify the expression cosh(ln t), we can use the properties of hyperbolic functions. First, we need to express ln t in terms of hyperbolic functions. Using the identity cosh(x) = (e^x + e^(-x))/2, we can rewrite ln t as ln t = (ln t + ln(t^(-1)))/2 = (ln t + (-1)ln t)/2 = (-ln(t))/2.
Next, we substitute the expression for ln t into the original expression cosh(ln t), giving us cosh((-ln(t))/2). Finally, we simplify cosh((-ln(t))/2) using the identity cosh(x) = (e^x + e^(-x))/2. Therefore, the simplified expression is (e^((-ln(t))/2) + e^((-(-ln(t))/2)))/2 = (e^((-ln(t))/2) + e^(ln(t)/2))/2.